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| == '''[[Global warming]]''' ==
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| ''by [[User:Gareth Leng|Gareth Leng]], [[User:Raymond Arritt|Raymond Arritt]], [[User:Robert Badgett|Robert Badgett]], [[User:Nereo Preto|Nereo Preto]], [[User:Anthony Sebastian|Anthony Sebastian]], and [[User:Benjamin Seghers|Benjamin Seghers]], <small>(and [[User:Milton Beychok|Milton Beychok]], [[User:David Finn|David Finn]], [[User:Greg Harris|Greg Harris]], [[User:Ed Poor|Ed Poor]], [[User:Larry Sanger|Larry Sanger]], [[User:John Stephenson|John Stephenson]] and [[User:Paul Wormer|Paul Wormer]])</small>''
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| | ==Footnotes== |
| [[Image:105582main GlobalWarming 2060 lg.jpg|right|thumb|Annual average global warming by the year 2060 simulated and plotted as color differences using EdGCM|250px]]
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| '''[[Global warming]]''' is the increase in the average temperature of the Earth's near-surface air and oceans in recent decades and its projected continuation. There is strong evidence that significant global warming is occurring; this evidence comes from direct measurements of rising surface air temperatures and subsurface ocean temperatures and from phenomena such as increases in average global sea levels, retreating glaciers, and changes to many physical and biological systems. It is likely that most of the warming in recent decades is attributable to human activity, particularly the burning of fossil fuels and deforestation.
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| Global average air temperature near the Earth's surface rose by 0.74 ± 0.18 °[[Celsius|C]] (1.33 ± 0.32 °F) from 1906 to 2005. The prevailing scientific view,
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| <ref name = Doran>See [http://tigger.uic.edu/~pdoran/012009_Doran_final.pdf Doran (2009)] 'Examining the Scientific Consensus
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| on Climate Change' for information on a poll of research-active climate scientists, other researchers and the public regarding the scientific consensus on global warming ''Eos'' 90: 21-2</ref> as represented by the science academies of the major industrialized nations<ref name = "academies">[http://nationalacademies.org/onpi/06072005.pdf Joint science academies’ statement: Global response to climate change]
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| *"There will always be uncertainty in understanding a system as complex as the world’s climate. However there is now strong evidence that significant global warming is occurring. The evidence comes from direct measurements of rising surface air temperatures and subsurface ocean temperatures and from phenomena such as increases in average global sea levels, retreating glaciers, and changes to many physical and biological systems. It is likely that most of the warming in recent decades can be attributed to human activities (IPCC 2001). This warming has already led to changes in the Earth's climate."</ref>
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| and the ''[http://www.ipcc.ch/ Intergovernmental Panel on Climate Change]'',<ref name=grida7>{{cite web | url=http://www.ipcc.ch/publications_and_data/ar4/wg1/en/spm.html|title=Summary for Policymakers|work=Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change|date=2007}}
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| *"Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations...Discernible human influences now extend to other aspects of climate, including ocean warming, continental-average temperatures, temperature extremes and wind patterns" </ref> it is very likely that most of the temperature increase since the mid-20th century has been caused by increases in atmospheric greenhouse gas concentrations produced by human activity. Climate models predict that average global surface temperatures will increase by a further 1.1 to 6.4 °C (2.0 to 11.5 °F) by the end of the century, relative to 1980–1999.<ref name=grida7/> The range of values reflects differing assumptions of future greenhouse gas emissions and results of models that differ in their sensitivity to increases in greenhouse gases.<ref name=grida7/>
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| Scientists have not yet quantitatively assessed the potential self-accelerating effects of global-warming itself, either on threshold or rate. Melting of permafrost, for example, causes increased production and atmospheric release of such newly produced as well as anciently stored methane gas, which “….packs a far greater warming punch than [carbon dioxide] (CO<sub>2</sub>),”<ref name=walker2007>Walker G (2007) [http://dx.doi.org/10.1038/446718a Climate Change 2007: A world melting from the top down] ''Nature'' 446:718-21</ref> possibly as much as 25 times that of CO<sub>2</sub> per unit mass.<ref name=simpson2009>Simpson (2009) [http://www.ScientificAmerican.com/Earth3 "The Peril Below the Ice"] ''Scientific American Earth 3.0'' pp 30-7</ref>
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| An increase in global temperatures will cause the sea level to rise, glaciers to retreat, sea ice to melt, and changes in the amount, geographical distribution and seasonal pattern of precipitation. There may also be changes in the frequency and intensity of extreme weather events. These will have many practical consequences, including changes in agricultural yields and impacts on human health.<ref>[http://www.ipcc.ch/publications_and_data/ar4/wg2/en/ch19s19-3-6.html Schneider ''et al.'' (2007)]. [http://www.ipcc.ch/publications_and_data/ar4/wg2/en/ch19.html Assessing key vulnerabilities and the risk from climate change]. In Parry ML ''et al.'' (eds) ''[http://www.ipcc.ch/publications_and_data/ar4/wg2/en/contents.html Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change]'' Cambridge University Press pp 779-810
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| *"There is new and stronger evidence of observed impacts of climate change on unique and vulnerable systems (such as polar and high-mountain communities and ecosystems), with increasing levels of adverse impacts as temperatures increase (very high confidence).
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| *There is new evidence that observed climate change is likely to have already increased the risk of certain extreme events such as heatwaves, and it is more likely than not that warming has contributed to the intensification of some tropical cyclones, with increasing levels of adverse impacts as temperatures increase (very high confidence).
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| *The distribution of impacts and vulnerabilities is still considered to be uneven, and low-latitude, less-developed areas are generally at greatest risk due to both higher sensitivity and lower adaptive capacity; but there is new evidence that vulnerability to climate change is also highly variable within countries, including developed countries." </ref> Scientific uncertainties include the extent of climate change expected in the future, and how changes will vary around the globe. There is political and public debate about what action should be taken to reduce future warming or to adapt to its consequences. The Kyoto Protocol, an international agreement aimed at reducing greenhouse gas emissions, was adopted by 169 nations.
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| ''[[Global warming|.... (read more)]]''
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| ! style="text-align: center;" | [[Global warming#References|notes]]
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In computational molecular physics and solid state physics, the Born-Oppenheimer approximation is used to separate the quantum mechanical motion of the electrons from the motion of the nuclei. The method relies on the large mass ratio of electrons and nuclei. For instance the lightest nucleus, the hydrogen nucleus, is already 1836 times heavier than an electron. The method is named after Max Born and Robert Oppenheimer[1], who proposed it in 1927.
Rationale
The computation of the energy and wave function of an average-size molecule is a formidable task that is alleviated by the Born-Oppenheimer (BO) approximation.The BO approximation makes it possible to compute the wave function in two less formidable, consecutive, steps. This approximation was proposed in the early days of quantum mechanics by Born and Oppenheimer (1927) and is indispensable in quantum chemistry and ubiquitous in large parts of computational physics.
In the first step of the BO approximation the electronic Schrödinger equation is solved, yielding a wave function depending on electrons only. For benzene this wave function depends on 126 electronic coordinates. During this solution the nuclei are fixed in a certain configuration, very often the equilibrium configuration. If the effects of the quantum mechanical nuclear motion are to be studied, for instance because a vibrational spectrum is required, this electronic computation must be repeated for many different nuclear configurations. The set of electronic energies thus computed becomes a function of the nuclear coordinates. In the second step of the BO approximation this function serves as a potential in a Schrödinger equation containing only the nuclei—for benzene an equation in 36 variables.
The success of the BO approximation is due to the high ratio between nuclear and electronic masses. The approximation is an important tool of quantum chemistry, without it only the lightest molecule, H2, could be handled; all computations of molecular wave functions for larger molecules make use of it. Even in the cases where the BO approximation breaks down, it is used as a point of departure for the computations.
Historical note
The Born-Oppenheimer approximation is named after M. Born and R. Oppenheimer who wrote a paper
[Annalen der Physik, vol. 84, pp. 457-484 (1927)] entitled: Zur Quantentheorie der Molekeln (On the Quantum Theory of Molecules). This paper describes the separation of electronic motion, nuclear vibrations, and molecular rotation. A reader of this paper who expects to find clearly delineated the BO approximation—as it is explained above and in most modern textbooks—will be disappointed. The presentation of the BO approximation is well hidden in Taylor expansions (in terms of internal and external nuclear coordinates) of (i) electronic wave functions, (ii) potential energy surfaces and (iii) nuclear kinetic energy terms. Internal coordinates are the relative positions of the nuclei in the molecular equilibrium and their displacements (vibrations) from equilibrium. External coordinates are the position of the center of mass and the orientation of the molecule. The Taylor expansions complicate the theory tremendously and make the derivations
very hard to follow. Moreover, knowing that the proper separation of vibrations and rotations was not achieved in this work, but only eight years later [by C. Eckart, Physical Review, vol. 46, pp. 383-387 (1935)] (see Eckart conditions), chemists and molecular physicists are not very much motivated to invest much effort into understanding the work by Born and Oppenheimer, however famous it may be. Although the article still collects many citations each year, it is safe to say that it is not read anymore, except maybe by historians of science.